Question

A code is formed using four of these letters: A, B, I, K, N, O, and T. (Note that the order of the letters in the code matters; for example, ABIK is a different code from BAIK. )
The size of the sample space is 1.)_________
A.120 B.360 C.840 D.1680
. The probability that the first three letters of the four-letter code are vowels is 2.)_________.
A.1/35 B.1/60 C.1/140 D.101/105

Answer 1

To answer this question, use permutation since the order of the letter matters. There are 7 letters and only 4 are to be used for the code. This  is a permutation of 7 taken 4 (7P4) which is equal to 840. Thus, the sample space is 840.
For the next questions, there are 3 vowels for as the first letter, only 6 letters are available for the second, 5 on the next, and 4 on the last. Multiplying these numbers give 360. To solve for probability, divide this number with the sample space. Thus, the answer is 3/7.